Achronim ask: There is a machlokes R’ Yochanan and Reish Lakish (Baba Kamma 21) whether isho m’shum chitzav or isho m’shum mamono, whether an arsonist is liable because lighting a fire is like shooting an arrow at something, or whether he is liable because lighting a fire is like letting an ox destroy someone else’s property. The Nimukei Yosef is mechadesh that according to R’ Yochanan, who holds isho m’shum chitzo, it is not at the moment the fire destroys (or the moment the arrow strikes its target) that the person becomes chayav, but rather it is from the moment the fire is lit (or the moment the arrow is released). It is the setting in motion of the process which is key (we discussed this a few years ago).
If so, R’ Yochanan l’shitaso who holds isho m’shum chitzo should also hold that the 9th of Av, when the fire was lit, is the key moment from which all else follows. Why did he think the fast should be on the 10th?
The Avnei Nezer answers that it is only with respect to the hischayvus of the individual that we look at the moment of the fire being lit; it is that moment which defines the individual as a poel, an actor, in the events that play out. However, when looking at the consequences of the events themselves, of course what occurs later may be far more significant than the initial moment.
The She’eiris Menachem quotes another interesting answer (he does not attribute it, though he says he heard it from someone). The Nimukei Yosef writes that just like you can’t pull an arrow back midflight, so too, what happens after a fire is lit is outside a person’s control -- liability occurs only for that first moment when a person has the ability to determine whether to strike the match or not or whether to release the arrow or not.
The gemara records that Hashem promised that just as He destroyed the Mikdash with fire, so too will He ultimately rebuild it with fire –- Hashem attributes the fire of destruction to himself, kavyachol.
A human being may not be able to pull an arrow back midflight, or stop a fire once it has been lit, but nothing is outside Hashem’s power. It is only when speaking of human action that we need to limit our focus to the first moment alone. When speaking about G-d, the entire process can be taken into consideration.